Increasing boiling heat transfer using low thermal conductivity materials

ABSTRACT

An apparatus having a heat transfer surface for transfer of heat from the apparatus to a liquid. The heat transfer surface includes at least two different materials and at least two of said materials have different thermal conductivities. A method of boiling at least one liquid which provides increased heat transfer from a heat transfer surface of an apparatus to a liquid comprising a step of boiling said liquid in contact with the apparatus, is also disclosed. Also described is a method of tuning a heat transfer surface by forming the heat transfer surface using at least two different materials having different thermal conductivities arranged in a predetermined spatial relationship including a spacing between the portions of one said material that is from about 0.1λ C  to about 5λ C , wherein λ C  is a capillary length of a bubble of a predetermined liquid to be boiled using said heat transfer surface.

STATEMENT OF GOVERNMENT INTEREST

This invention was made with government support under Grant No. 1454407 awarded by the National Science Foundation. The Government has certain rights in this invention.

BACKGROUND Field of the Invention

The present invention is directed to increasing heat transfer to a liquid during boiling by providing a heat transfer surface including a combination of a high thermal conductivity material and a low thermal conductivity material to form the heating surface. More specifically, the invention provides a heat transfer surface with a spatial variation in the temperature profile of the surface to aid bubble dynamics during boiling.

Description of the Related Technology

Boiling is a well-studied mode of heat transfer and is common in many industrial applications. The large amount of energy in the form of latent heat makes phase change phenomena, like boiling, of critical importance to the development of next-generation thermal and energy systems. Boiling heat transfer is used in many applications, including the production of electricity, chemical processing, and high-heat flux thermal management. Due to its prevalence, and the important role it plays in numerous industries, the enhancement of boiling heat transfer has been studied for decades. During boiling, heat is transferred from a hot surface to a cooler fluid by (1) evaporation across liquid-vapor interfaces, (2) transient conduction, and (3) the micro-convection generated by the nucleation, growth, and departure of vapor bubbles. The rate of heat transfer at a given wall superheat (the difference in surface and fluid saturation temperatures) is governed by a variety of factors including nucleation site density, as well as bubble dynamics and the ebullition cycle. The efficiency of boiling is quantified by the heat transfer coefficient (HTC), defined as the ratio of the surface heat flux to the superheat temperature, the temperature difference between the solid and the saturated fluid. During boiling, there is a finite rate at which heat can be dissipated from any surface. This maximum is the critical heat flux (CHF). CHF, also referred to as the boiling crisis, occurs when the production of vapor cannot be adequately balanced by the amount of liquid returning to the heated surface. When this occurs the surface undergoes dry-out, where an insulating layer of vapor blankets the solid surface. This leads to an immediate, uncontrollable, and drastic increase in surface temperature with dangerous and potentially catastrophic consequences, such as the destruction of electronic components or the meltdown of a nuclear reactor.

Understanding and improving HTC and CHF in boiling systems has been extensively studied for decades, including the development of a variety of enhancement strategies. See, Bergles, A. E. & Manglik, R. M. Current Progress and New Developments in Enhanced Heat and Mass Transfer. Journal of Enhanced Heat Transfer 20, 1-15 (2013). Traditionally, the use of enhanced surfaces has been primarily focused on the creation of structures and complex geometries machined into, or attached onto, the boiling surface such as porous materials, sintered wires and meshes, as well as mechanically deformed structures. See, Li, C. & Peterson, G. P. Parametric study of pool boiling on horizontal highly conductive microporous coated surfaces. Journal of Heat Transfer-Transactions of the Asme 129, 1465-1475 (2007) and Marto, P. J. & Lepere, V. J. Pool Boiling Heat-Transfer from Enhanced Surfaces to Dielectric Fluids. Journal of Heat Transfer-Transactions of the Asme 104, 292-299 (1982).

With the development of increasingly precise fabrication tools, micro/nano-structured surface coatings have been explored in recent years, showing substantial increases in boiling performance. A variety of microscale and nanoscale wires, rods, posts, and other structures have been fabricated on silicon chips and shown to enhance HTC and CHF of water anywhere from 50% to 300%, depending on the working fluid. See, O'Hanley, H. et al. Separate effects of surface roughness, wettability, and porosity on the boiling critical heat flux. Applied Physics Letters 103, 024102-5 (2013); Rahman, M. M., Ölçero{hacek over (g)}lu, E. & McCarthy, M. Role of Wickability on the Critical Heat Flux of Structured Superhydrophilic Surfaces. Langmuir 30, 11225-11234 (2014); and Zou, A. & Maroo, S. C. Critical height of micro/nano structures for pool boiling heat transfer enhancement. Applied Physics Letters 103, 221602 (2013). Similarly, micro/nano-structures on copper and other metals have also been demonstrated. See, Cooke, D. & Kandlikar, S. G. Effect of open microchannel geometry on pool boiling enhancement. International Journal of Heat and Mass Transfer 55, 1004-1013 (2012) and Rahman, M. M., Ölçero{hacek over (g)}lu, E. & McCarthy, M. Scalable Nanomanufacturing of Virus-templated Coatings for Enhanced Boiling. Advanced Materials Interfaces 1, 1300107 (2014).

The role that surface structures play in boiling enhancement has been attributed to a variety of factors, including capillary wicking, increased nucleation site densities, and increased contact line pinning. Additionally, notable increases in HTC have been reported using embossed copper microstructures with specific contoured shapes. See, Kandlikar, S. G. Controlling bubble motion over heated surface through evaporation momentum force to enhance pool boiling heat transfer. Applied Physics Letters 102, 051611-5 (2013). These complex microscale shapes use evaporation momentum force to promote the separation of liquid and vapor flow paths and enhance micro-convection.

A CHF of 200 W/cm2 using silicon nanowires, with diameters of 20-300 nm and lengths of 40-50 μm, chemically etched into flat silicon substrates has been reported. See, Chen, R., Lu, M.-C., Srinivasan, V., Wang, Z., Cho, H. H., and Majumdar, A., Nanowires for Enhanced Boiling Heat Transfer, Nano Letters, vol. 9, no. 2, pp. 548-553, 2009. A CHF of 208 W/cm2 for dry etched silicon micropillar arrays with a 5 μm diameter, a 10 μm center-to-center pitch, and a 20 μm height has also been reported. See, Chu, K.-H., Enright, R., and Wang, E. N., Structured Surfaces for Enhanced Pool Boiling Heat Transfer, Applied Physics Letters, vol. 100, no. 24, 241603, 2012. This was extended using hierarchical surfaces, comprised of nanostructures oxides coating microstructured post arrays, to show a CHF of 250 W/cm2. See, Chu, K.-H., Joung, Y. S., Enright, R., Buie, C. R., Wang, E. N., Hierarchically Structured Surfaces for Boiling Critical Heat Flux Enhancement, Applied Physics Letters, vol. 102, no. 15, 151602, 2013. Similar results using nanostructured coatings on a variety of metallic substrates have also been shown. These examples represent increases in CHF of up to 225% as compared to bare substrates, via the addition of micro/nano-scale surface structures. A variety of physical explanations for these enhancements have been proposed, including the increase of nucleation sites, contact line pinning, as well as capillary wicking. Interestingly, nanostructures were shown to increase or decrease HTC depending on the substrate to which the coatings were applied.

Engineered surfaces have also been shown to increase HTC using a variety of surface designs and enhancement mechanisms. These include increasing nucleation using microstructures and low-surface-energy materials, as well as promoting the order of liquid and vapor flow paths. Betz et al. fabricated biphilic and superbiphilic surfaces by adding a pattern of hydrophobic polytetrafluoroethylene (PTFE) islands (45 μm diameter and 100 μm center-to-center pitch) on flat and nanostructured silicon surfaces, respectively. See, Betz, A. R., Xu, J., Qiu, H., and Attinger, D., Do Surfaces with Mixed Hydrophilic and Hydrophobic Areas Enhance Pool Boiling?, Applied Physics Letters, vol. 97, no. 14, 141909, 2010 and Betz, A. R., Jenkins, J., Kim, C.-J. C., and Attinger, D., Boiling Heat Transfer on Superhydrophilic, Superhydrophobic, and Superbiphilic Surfaces, International Journal of Heat and Mass Transfer, vol. 57, pp. 733-741, 2013. These surfaces with mixed wettability were shown to nucleate at low wall superheats, with up to a three-fold increase in nucleation site densities as compared to hydrophilic nanostructured surfaces. By decreasing the temperature required for the onset of nucleate boiling (ONB) and increasing nucleation sites, the maximum HTC was increased by up to 650%. By imparting spatial order to the liquid-vapor flow fields away from the surface, increases in both HTC and CHF have been shown using different techniques. Kandlikar fabricated contoured micro-scale surface features into copper substrates using an embossing technique showing an increase in maximum HTC of 740%, at a CHF increase of 150%. See, Kandlikar, S. G., Controlling Bubble Motion Over Heated Surface Through Evaporation Momentum Force to Enhance Pool Boiling Heat Transfer, Applied Physics Letters, vol. 102, no. 5, 051611, 2013. These enhancements were attributed to the creation of separate liquid and vapor pathways and an increase in nucleation site densities on the structured copper surface.

While structured surfaces have been shown to greatly increase boiling heat transfer, the reliability of these approaches for real-world applications is in question due to a variety of factors. All structured surfaces are inherently susceptible to mechanical failure (breaking of the micro/nano-structures), as well as fouling and clogging over time. During boiling, any and all contaminants within the fluid will inevitably be drawn into the structures. This will lead to clogging and filling of the small micro/nano-scale voids, and thus a loss of enhancement. Similarly, the robustness of extremely thin nanostructured coatings (≦1 μm) has not yet been demonstrated, leaving the potential for the coatings to be destroyed or altered over time via chemical reactions. The use of low-surface-energy materials to promote nucleation at small superheats has been successfully demonstrated as well, however these biphilic surfaces are prone to degradation of the thin non-wetting films. Additionally, they are not effective with all working fluids, in particular highly wetting fluids like FC-72. While doubly reentrant surfaces have been demonstrated to repel these highly wetting fluids, their use in biphilic designs for boiling enhancement has not yet been demonstrated. These enhancement techniques rely on surface properties and interfacial phenomena, which are inherently susceptible to degradation.

SUMMARY OF THE INVENTION

In one aspect, the invention is directed to an apparatus that defines a heat transfer surface for transfer of heat from the apparatus to a liquid. The heat transfer surface includes at least two different materials at least two of which have significantly different thermal conductivities.

In a second aspect, the at least two different materials having different thermal conductivities are arranged in a predetermined spatial relationship relative to each other. The arrangement of these materials in this spatial relationship is designed to further increase the critical heat flux from the heat transfer surface to a liquid and/or the heat transfer coefficient of the heat transfer surface by creating a regularly repeating variation in the surface temperature.

In a third aspect, the present invention relates to a method of boiling at least one liquid which provides increased heat transfer from a heat transfer surface of an apparatus to a liquid. In the method, an apparatus that defines a heat transfer surface for transfer of heat from the apparatus to a liquid is provided. The heat transfer surface includes at least two different materials at least two of which have significantly different thermal conductivities. The heat transfer surface is heated while in contact with a liquid whereby the heat transfer from the heat transfer surface to the liquid is increased, relative to a heat transfer surface made from only one of the at least two said materials.

In a fourth aspect, the present invention relates to a method for increasing one or both of a critical heat flux from a heat transfer surface of an apparatus to a liquid and/or a heat transfer coefficient of the heat transfer surface. The method includes a step of providing an apparatus including at least two different materials at least two of which have significantly different thermal conductivities.

In a fifth aspect, the present invention relates to a method of tuning a heat transfer surface of an apparatus by forming the heat transfer surface using at least two different materials having different thermal conductivities arranged in a predetermined spatial relationship. The arrangement of these materials in this spatial relationship is designed to further increase the critical heat flux from the heat transfer surface to a liquid and/or the heat transfer coefficient of the heat transfer surface by providing a spacing between the materials having different thermal conductivities that is related to a capillary length of a bubble on the heat transfer surface. The capillary length is the characteristic length scale of an interface subject to both surface tension and gravitational forces.

In a preferred aspect the heat transfer surface is a flat or substantially flat surface that generates a spatial variation in temperature of the heat transfer surface at least when heat is provided to the heat transfer surface. In one embodiment, the spatial variation in the temperature of the heat transfer surface is non-uniform.

These and other aspects of the invention are described below and in the enclosed document.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows pictures of a bi-conductive surface with two and twelve divisions per centimeter.

FIG. 2 is a thermal circuit diagram for a segment of a bi-conductive surface showing the relevant conductive and convective resistances between the base copper and the saturated fluid.

FIG. 3 shows scanning electron microscope (SEM) images of low-conductivity epoxy divisions embedded in high-conductivity copper.

FIG. 4 is a schematic of the resulting flow field where spatial variations in wall superheat temperature, ΔT(x), promote spatial ordering.

FIG. 5 is an SEM image of the result of nucleate boiling showing control over the nominal bubble diameter during lateral coalescence.

FIG. 6 is a diagram of the onset of nucleate boiling.

FIG. 7a shows high-speed time lapse images and corresponding diagrams of the lateral coalescence of attached vapor bubbles on bi-conductive surfaces.

FIG. 7b shows high-speed time lapse images and corresponding diagrams of the lateral coalescence of attached vapor bubbles on a comparative example of bare copper surfaces.

FIG. 8 shows graphs of results for heat flux and heat transfer coefficient as a function of wall superheat temperature.

FIG. 9A shows a graph of the percent increase in critical heat flux (CHF) for bi-conductive surfaces as compared to bare copper surfaces.

FIG. 9B shows a graph of the percent increase heat transfer coefficient (HTC) for bi-conductive surfaces as compared to bare copper surfaces.

FIG. 10 shows high-speed imaging of nucleate boiling at ˜10-15 W/cm² on a bare copper surface and on bi-conductive surfaces with the N=4 cm⁻¹, N=6 cm⁻¹, and N=12 cm⁻¹ designs.

FIG. 11A is a schematic representation of the pool boiling experimental test apparatus set-up used in some of the examples.

FIG. 11B is a schematic representation of the wicking test set-up used in some of the examples.

FIG. 12A shows SEM images of a comparative example nanostructured CuO surfaces at two different magnifications. The scale bars are 10 μm and 2 μm in length.

FIG. 12B shows heat flux results for a comparative example nanostructured CuO surfaces as compared to bare copper surfaces

FIG. 12C shows heat transfer coefficient results for a comparative example nanostructured CuO surfaces as compared to bare copper surfaces.

FIG. 13A shows high-speed imaging of the wicking measurement technique used for a comparative example.

FIG. 13B shows wicked volume as a function of time for a comparative example, calculated by tracking the high-speed images of the displaced meniscus in the tube. The inset shows the maximum initial wicked volume flow rate, where t=0 represents the beginning of the wicking phase.

FIG. 13C shows the apparent wetted area of a comparative example as a function of time, where the droplet spreading phase (−5 ms<t<0 ms) occurs entirely before the liquid wicking phase (t>0 ms).

FIG. 14A shows SEM images of comparative example nanostructured nickel coatings fabricated using biotemplating, as well as patterned conformal PTFE films (˜10-20 nm thick). The scale bars are 2 μm and 1 μm in length.

FIG. 14B shows boiling results for heat flux as compared to the performance of comparative example superhydrophilic nanostructured surfaces.

FIG. 14C shows boiling results for heat transfer coefficient as compared to the performance of comparative example superhydrophilic nanostructured surfaces.

FIG. 15A is a picture of high-conductivity copper substrates with embedded lines of non-conductive epoxy.

FIG. 15B shows SEM images of the surface cross section and epoxy dimensions.

FIG. 15C shows SEM images for the experimentally determined optimal spacing for water.

FIG. 15D is a schematic representation of the desired flow field of ordered liquid and vapor pathways above a bi-conductive surface.

FIG. 16A shows the heat flux as compared to bare copper surfaces with no epoxy divisions.

FIG. 16B shows the heat transfer coefficient as compared to bare copper surfaces with no epoxy divisions.

FIG. 17A is a schematic representation of the nanostructured bi-conductive surfaces.

FIG. 17B is a schematic representation of the nanostructured bi-conductive biphilic surfaces.

FIG. 17C is a SEM image of a nanostructured bi-conductive biphilic surface showing the CuO nanostructures. The scale bar is 500 μm in length.

FIG. 17D is a magnification of the interface separating the superhydrophilic CuO nanostructures, and the superhydrophobic PTFE-coated nanostructures as shown in FIG. 17C. The scale bar is 4 μm in length.

FIG. 17E is a schematic representation of the desired flow field where nucleation is selectively promoted and suppressed, while the nanostructures provide capillary wicking.

FIG. 18A is a graph of heat flux as compared with the performance of bare copper, surface with nanostructured CuO only, and surfaces with bi-conductivity only.

FIG. 18B is a graph of heat transfer coefficient as compared with the performance of bare copper, surface with nanostructured CuO only, and surfaces with bi-conductivity only.

FIG. 19 shows SEM images of comparative example CuO nanostructured surfaces at two different magnifications.

FIG. 20 is a schematic diagram of a pool boiling experimental apparatus.

FIG. 21 shows graphs of CHF and HTC when DI water was used.

FIG. 22 shows graphs of CHF and HTC when water having 7 nm particles was used.

FIG. 23 shows graphs of CHF and HTC when water having 200 nm particles was used.

FIG. 24 shows graphs of CHF and HTC when water having 0.5 μm-10 μm particles was used.

FIG. 25 shows a graph of HTC v. CHF for comparative example bare copper with particles of varying sizes in the water.

FIG. 26 shows a graph of HTC v. CHF for comparative example CuO nanostructured surfaces with particles of varying sizes in the water.

FIG. 27 is a SEM image of comparative example CuO nanaostructured surface after boiling with 200 nm particles.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

For illustrative purposes, the principles of the present invention are described by referencing various exemplary embodiments thereof. Although certain embodiments of the invention are specifically described herein, one of ordinary skill in the art will readily recognize that the same principles are equally applicable to, and can be employed in other apparatuses and methods. Before explaining the disclosed embodiments of the present invention in detail, it is to be understood that the invention is not limited in its application to the details of any particular embodiment shown. The terminology used herein is for the purpose of description and not of limitation. Further, although certain methods are described with reference to certain steps that are presented herein in certain order, in many instances, these steps may be performed in any order as may be appreciated by one skilled in the art, and the methods are not limited to the particular arrangement of steps disclosed herein.

It must be noted that as used herein and in the appended claims, the singular forms “a”, “an”, and “the” include plural references unless the context clearly dictates otherwise. As well, the terms “a” (or “an”), “one or more” and “at least one” can be used interchangeably herein. It is also to be noted that the terms “comprising”, “including”, and “having” can be used interchangeably.

Unless otherwise indicated, all numbers expressing quantities of ingredients, properties such as molecular weight, percent, ratio, reaction conditions, and so forth used in the specification and claims are to be understood as being modified in all instances by the term “about,” whether or not the term “about” is present. Accordingly, unless indicated to the contrary, the numerical parameters set forth in the specification and claims are approximations that may vary depending upon the desired properties sought to be obtained by the present disclosure. At the very least, and not as an attempt to limit the application of the doctrine of equivalents to the scope of the claims, each numerical parameter should at least be construed in light of the number of reported significant digits and by applying ordinary rounding techniques. Notwithstanding that the numerical ranges and parameters setting forth the broad scope of the disclosure are approximations, the numerical values set forth in the specific examples are reported as precisely as possible. Any numerical value, however, inherently contains certain errors necessarily resulting from the standard deviation found in their respective testing measurements.

It is to be understood that each component, compound, substituent, or parameter disclosed herein is to be interpreted as being disclosed for use alone or in combination with one or more of each and every other component, compound, substituent, or parameter disclosed herein.

It is also to be understood that each amount/value or range of amounts/values for each component, compound, substituent, or parameter disclosed herein is to be interpreted as also being disclosed in combination with each amount/value or range of amounts/values disclosed for any other component(s), compounds(s), substituent(s), or parameter(s) disclosed herein and that any combination of amounts/values or ranges of amounts/values for two or more component(s), compounds(s), substituent(s), or parameters disclosed herein are thus also disclosed in combination with each other for the purposes of this description.

It is further understood that each lower limit of each range disclosed herein is to be interpreted as disclosed in combination with each upper limit of each range disclosed herein for the same component, compounds, substituent, or parameter. Thus, a disclosure of two ranges is to be interpreted as a disclosure of four ranges derived by combining each lower limit of each range with each upper limit of each range. A disclosure of three ranges is to be interpreted as a disclosure of nine ranges derived by combining each lower limit of each range with each upper limit of each range, etc. Furthermore, specific amounts/values of a component, compound, substituent, or parameter disclosed in the description or an example is to be interpreted as a disclosure of either a lower or an upper limit of a range and thus can be combined with any other lower or upper limit of a range or specific amount/value for the same component, compound, substituent, or parameter disclosed elsewhere in the application to form a range for that component, compound, substituent, or parameter.

The term, “substantially” as used herein includes a variation of up to 5%, or a variation of up to 2% or a variation of up to 1% from the specified parameter or shape.

It is also to be understood that all aspects of the apparatus disclosed herein can be implemented in methods of the present invention even if such a method is not expressly set forth herein.

It has been found that the CHF and HTC can be enhanced by using surfaces with in-plane variations in substrate thermal conductivity. FIG. 1 shows a fabricated bi-conductive surface with two and twelve divisions per centimeter. The “bi-conductive” surfaces are comprised of one or more low-conductivity materials represented by the thinner lines in FIG. 1, embedded into one or more high-conductivity substrates represented by the thicker portions in FIG. 1, and therefore rely on bulk properties rather than surface properties to enhance boiling. These surfaces create spatial variations in the surface temperature during boiling, and by tuning the wavelength of these variations to coincide with the capillary length, increases in HTC and CHF of greater than a factor 5× and 2×, respectively, have been achieved. Not to be bound by theory, these results may be explained by an examination of the resulting liquid and vapor flow fields, as well as enhanced bubble dynamics. This enhancement mechanism holds the potential for creating robust and reliable surfaces for high-efficiency and high heat flux boiling applications that will have long lifetimes.

The present apparatus increases boiling heat transfer by incorporating low-conductivity materials at the interface between the surface and fluid. By embedding an array of non-conductive material into a high-conductivity substrate, in-plane variations in the local surface temperature are created. During boiling the surface temperature varies spatially across the substrate, alternating between high and low values, and thereby promotes the organization of distinct liquid and vapor flows. By systematically tuning the peak-to-peak wavelength of this spatial temperature variation, a resonance-like effect is seen at a value equal to the capillary length of the fluid. In a preferred embodiment, replacing about 18% of the surface with a non-conductive epoxy results in a greater than 5× increase in heat transfer rate at a given superheat temperature. This drastic and counterintuitive increase is shown to be due to optimized bubble dynamics, where ordered pathways allow for efficient removal of vapor and the return of replenishing liquid. The use of engineered thermal gradients represents a novel approach to create high-efficiency and high-heat-flux boiling surfaces which are naturally insensitive to fouling and degradation as compared to other approaches.

To understand the variations in surface temperature and the relative rates of heat transfer through the sections of low- and high-conductivity materials of the bi-conductive surfaces, a first order thermal circuit analysis has been carried out using the preferred materials which are epoxy and copper. FIG. 2 shows a segment of a bi-conductive surface with an embedded epoxy division approximated with a rectangular cross section. The epoxy dimensions are W_(E)=0.42 mm and D=0.29 mm, as measured in SEM imaging (FIG. 3). The width of the copper section is given by W_(C)=P−W_(E) where the pitch P varies for each surface from 0.96 mm to 3.7 mm. This results in copper widths of W_(C)=0.54 mm−3.28 mm for the six bi-conductive surfaces that were fabricated and tested.

Equations S1 and S2 give the convective thermal resistances in the water above the epoxy and copper sections, while Equations S3 and S4 give the conductive resistances through the epoxy and copper. In Equations S1-S4, k is the thermal conductivity, L is the length of the epoxy division (also the edge length of the sample), and the subscripts or superscripts E and C are used to denote the epoxy and copper, respectively. It is assumed in this analysis that k_(C)=400 W/mK and k_(E)=1 W/mK. The heat transfer coefficient in the fluid is given by h, and assumed to be constant across the whole surface.

$\begin{matrix} {R_{conv}^{E} = {\frac{1}{{hA}_{E}} = \frac{1}{{hW}_{E}L}}} & ({S1}) \\ {R_{conv}^{C} = {\frac{1}{{hA}_{C}} = \frac{1}{{hW}_{C}L}}} & ({S2}) \\ {R_{cond}^{E} = {\frac{D}{k_{E}A_{E}} = \frac{D}{k_{E}W_{E}L}}} & ({S3}) \\ {R_{cond}^{C} = {\frac{D}{k_{C}A_{C}} = \frac{D}{k_{C}W_{C}L}}} & ({S4}) \end{matrix}$

The total heat transfer rate passing through this segment of the bi-conductive surface is given by q_(T), with some portion of that passing through the epoxy (q_(E)) and some passing through the copper (q_(C)), such that:

q _(T) =q _(E) +q _(C)  (S5)

Using this thermal circuit model, the fraction of the heat transfer passing through the epoxy divisions can be calculated as:

$\begin{matrix} {{\frac{q_{E}}{q_{T}} = {\frac{q_{E}}{q_{E} + q_{C}} = \frac{1}{1 + \left( {q_{C}/q_{E}} \right)}}},} & ({S6}) \end{matrix}$

where q_(C)/q_(E) is evaluated as:

$\begin{matrix} {\frac{q_{C}}{q_{E}} = {\frac{\left( {T_{B} - T_{sat}} \right)/\left( {R_{cond}^{C} + R_{conv}^{C}} \right)}{\left( {T_{B} - T_{sat}} \right)/\left( {R_{cond}^{E} + R_{conv}^{E}} \right)} = {\frac{R_{cond}^{E} + R_{conv}^{E}}{R_{cond}^{C} + R_{conv}^{C}}.}}} & ({S7}) \end{matrix}$

Combining equations S5 and S7 yields:

$\begin{matrix} {\frac{q_{E}}{q_{T}} = {1 + {\frac{W_{C}}{W_{E}}{\frac{1 + {{hD}/k_{E}^{- 1}}}{1 + {{hD}/k_{C}}}.}}}} & ({S8}) \end{matrix}$

Additionally, the ratio of the wall superheat above the epoxy to the superheat above the copper can also be solved for as:

$\begin{matrix} {{\frac{\Delta \; T_{{sat},E}}{\Delta \; T_{{sat},C}} = {\frac{T_{E} - T_{sat}}{T_{C} - T_{sat}} = \frac{q_{E}R_{conv}^{E}}{q_{C}R_{conv}^{C}}}},} & ({S9}) \end{matrix}$

which reduces to:

$\begin{matrix} {\frac{\Delta \; T_{{sat},E}}{\Delta \; T_{{sat},C}} = {\frac{1 + {{hD}/k_{C}}}{1 + {{hD}/k_{E}}}.}} & ({S10}) \end{matrix}$

Evaluation of equations S8 and S10 provides a first order estimate of the magnitude of the heat transfer rate through the epoxy divisions, as well as the ability of the bi-conductive surfaces to suppress the wall superheat above the epoxy divisions. It can be shown that during the nucleate boiling process, the percentage of heat transferred across the epoxy division is extremely small.

As such, the wall superheat temperature above the low-conductivity material divisions will be notably reduced as compared to that experienced over the high conductivity substrate. At low average wall superheats, prior to bubble nucleation, these in-plane temperature variations will drive natural convection flows aligned with the low-conductivity material divisions similar to Rayleigh-Bérnard convection rolls. It has been shown that this sort of flow instability is immediately triggered for any finite superheating with a spatially varying surface temperature.

The resulting flow-field draws cooler liquid down toward the surface from above the low divisions, while warmer fluid rises from above the hot high conductivity substrate. At these early stages of heat the counter-rotating flows will produce a stagnation point in the center of the high conductivity substrate, resulting in a local minimum in convective heat transfer and therefore a local maximum in surface temperature. As the wall superheat is increased this local maximum temperature promotes bubble nucleation along the center of the high conductivity substrate regions. This results in the formation of an ordered flow-field, as shown schematically in FIG. 4, which persists at increasing thermal loadings. The in-plane variations in wall superheat take a periodic form with a wavelength equal to the pitch P between low-conductivity material divisions. This superheat wavelength dictates the nature and location of the ordered pathways of escaping vapor and replenishing liquid returning to the surface during nucleate boiling. FIG. 5 shows an image of the onset of nucleate boiling, where the first few nucleation sites are activated on a bi-conductive surface (N=4 cm⁻¹) at a wall superheat of ˜5 K. As can be seen, the vapor bubbles preferentially nucleate near the center of the high conductivity substrate due to the local maximum in surface temperature. This is consistently seen for all of the surfaces tested, and demonstrates that the wettability of the low-conductivity material is not promoting nucleation due to a lower surface energy.

FIG. 6 shows how the superheat wavelength equal to the pitch, P, imparts a level of control over the bubble diameter during lateral coalescence. By ordering nucleation sites and liquid return pathways, the size of bubbles undergoing lateral coalescence across a low-conductivity material division is tuned to nominally coincide with the superheat wavelength.

The enhancements shown here have been attributed to the ability of in-plane variations in wall superheat to impart order to the resulting liquid and vapor flows, leading to high HTC and a delay in CHF. By reducing the superheat temperature in the vicinity of the low-conductivity materials, the epoxy divisions suppress nucleation and remain wetted during boiling. While this reduces the local heat transfer rate near the epoxy, it increases the global heat transfer rate over the entire surface by imparting spatial ordering and enhanced bubble dynamics. For this order to be maintained the cold epoxy divisions must remain wetted at all times. FIGS. 7A and 7B show time-lapse imaging of vapor bubbles undergoing lateral coalescence, and demonstrates the ability of the epoxy divisions to remain wetted during boiling.

In all of the imaging of bare copper surfaces, the three-phase contact line beneath a bubble undergoes visible in-plane motion during lateral coalescence. This behavior, however, is not seen on the bi-conductive surfaces where the epoxy divisions remain wetted at all times and effectively create boundaries that the three-phase contact lines do not cross. This behavior is essential for creating and maintaining ordered pathways of escaping vapor and replenishing liquid and is seen as the key contributor to boiling enhancement. Several researchers have observed and characterized the complex motion of contact lines during nucleate boiling and boiling crisis. These include the work by Kim et al. and Jung et al. using IR thermometry to visualize the liquid-solid interface and measure contact line length, density, and speed. See, Kim, H., Park, Y. & Buongiorno, J. Measurement of wetted area fraction in subcooled pool boiling of water using infrared thermography. Nuclear Engineering and Design 264, 103-110 (2013) and Jung, J., Kim, S. J. & Kim, J. Observations of the Critical Heat Flux Process During Pool Boiling of FC-72. Journal of Heat Transfer-Transactions of the ASME 136 (2014).

In addition to spatially ordering the escaping vapor and returning liquid flows, the epoxy divisions promote the coalescence-induced departure of laterally merging bubbles. FIG. 7A shows the coalescence of two bubbles of a size of about 2 mm bridging over an epoxy division. As the two bubbles merge the underlying epoxy division between them remains wetted at all times. A thin liquid layer remains on the cold epoxy surface and the non-wetted base areas below each bubble do not merge, collapse, or otherwise move during the process. The resulting bubble deforms due to surface tension and is quickly ejected from the surface. The low temperature epoxy inhibits the inward lateral merging of the non-wetted bases, and helps draw replenishing liquid underneath the bubble thus promoting departure. Conversely, FIG. 7B shows time lapse imaging during pool boiling on bare copper surfaces at a comparable heat flux, where three distinct lateral coalescence events are visible. The result is a new non-wetted base area beneath the larger coalesced bubble that is still attached to the surface. While this high-speed imaging is conducted at relatively low heat fluxes, it does provide insight into the mechanism driving boiling enhancement on bi-conductive surfaces. The behaviors visualized at low fluxes, along with the pool boiling results shown in FIG. 8, can be used to draw conclusions regarding the nature of enhancement across all boiling regimes up to CHF.

The enhancement mechanisms proposed here are inherently linked to the wavelength of the spatial variations in surface superheat wavelength, P, as illustrated in FIG. 6. To probe the effect of this wavelength on boiling performance, the pitch between epoxy divisions has been systematically varied. The percent increase in CHF and HTC of the bi-conductive surfaces relative to bare copper is plotted in FIGS. 9A and 9B against the superheat wavelength, P, normalized by the capillary length, λ_(C). The capillary length is the characteristic length scale of an interface subject to both surface tension and gravitational forces, and for a bubble is given by:

$\begin{matrix} {\lambda_{C} = \sqrt{\frac{\sigma}{g\left( {\rho_{l} - \rho_{v}} \right)}}} & (1) \end{matrix}$

where σ is the surface tension at the interface, g is the acceleration of gravity, and ρ_(i) and ρ_(v) are the densities of the liquid and vapor phases, respectively. The relative importance of surface tension and buoyancy (gravitational) forces on a bubble is captured through the non-dimensional Bond number, Bo, given by:

$\begin{matrix} {{Bo} = \frac{L_{C}^{2}{g\left( {\rho_{l} - \rho_{v}} \right)}}{\sigma}} & (2) \end{matrix}$

where L_(c) is the characteristic length. Defining the Bond number using the wavelength of the superheat variations, P, as the characteristic length of the surface results in:

$\begin{matrix} {{Bo}_{P}^{1/2} = {{P\sqrt{\frac{g\left( {\rho_{l} - \rho_{v}} \right)}{\sigma}}} = {\frac{P}{\lambda_{C}}.}}} & (3) \end{matrix}$

FIGS. 9A and 9B show the importance of Bond number and capillary length on the boiling enhancement of bi-conductive surfaces, where all fluid properties are evaluated at the saturation temperature and the edge length of the sample is used as the characteristic length for bare copper. A clear maximum in performance is seen when the superheat wavelength (and pitch between epoxy divisions, P) coincides with the capillary length of the fluid, and the Bond number approaches unity. This optimal wavelength can be explained by examining the nominal bubble departure diameter during boiling. This is traditionally characterized by defining the Bond number using the bubble departure diameter, D, as the characteristic length. Numerous correlations exist to predict bubble departure using the non-dimensional departure diameter given by Bo_(D) ^(1/2). These include the classical works of Fritz, and Cole and Rohsenow, which have shown good agreement with experimental results for decades. See, Fritz, W. Berechnung des Maximalvolume von Dampfblasen. Phys. Z. 36, 379-388 (1935) and Cole, R., Rohsenow, W. M. Correlation of bubble departure diameters for boiling of saturated liquids. Chem. Eng. Prog. Symp. Ser. 65, 211-213 (1968). Fritz's empirical correlation relates the departure diameter to the contact angle of the surface, θ, and is given by:

Bo _(D) ^(1/2)=0.0208θ.  (4)

Cole and Rohsenow's correlation for water is given by:

Bo _(D) ^(1/2)=1.5×10⁻⁴ Ja* ^(5/4).  (5)

The effects of sensible and latent heat are incorporated in this correlation through the use of the modified Jakob number defined as:

$\begin{matrix} {{Ja}^{*} = \frac{\rho_{l}C_{pl}T_{Sat}}{\rho_{v}h_{fg}}} & (6) \end{matrix}$

where C_(pl) is the heat capacity of the liquid and h_(fg) is the latent heat of vaporization. Evaluating equations (4) and (5) for saturated water on copper results in values of Bo_(D) ^(1/2)=1.04±0.1 and Bo_(D) ^(1/2)=0.98±0.1, respectively, considering the uncertainties in contact angle and material properties. The bubble departure diameters predicted by both models closely match the optimal pitch between epoxy divisions found experimentally to be Bo_(P) ^(1/2)≈1.

These predictions show that as the wavelength of the variations in superheat, P, approaches the departure diameter of the bubbles, a resonance-like effect is seen leading to substantial increases in both HTC and CHF. FIG. 9B shows that this resonance-like enhancement in heat transfer is seen at the same wavelength for all phases of boiling. At a common wall superheat of ΔT=11 K, the heat transfer rates of the various surfaces range from 40-230 W/cm⁻² (FIG. 3A). This corresponds to a greater than 5× difference in vapor production rates between the highest and lowest performing surfaces. At a common heat flux of 91 W/cm⁻², the required wall superheat more than doubles across the surfaces tested, varying from 9 K to 19 K. At CHF, each surface is operating at distinctly different heat fluxes (from 91 W/cm⁻² to 230 W/cm⁻²) and wall superheats (from 11 K to 19 K). Yet in all three cases, the maximum HTC is observed for bi-conductive surfaces where the pitch between epoxy divisions, P, is equal to the capillary length, λ_(C).

Adding epoxy divisions and therefore reducing the area available for heat transfer by ˜18%, results in up to a 5× increase in heat transfer rate at a given superheat. This result is explained by examining the nature of the bubble nucleation, growth, and departure process. The addition of non-conductive epoxy imparts order to the resulting vapor and liquid flows, which helps draw cool liquid to the surface and promotes departure of nucleating bubbles. While less of the surface area is available to transfer heat, this spatial order enhances the ebullition cycle and also delays dry-out. FIG. 9B shows with the addition of two and four epoxy divisions per centimeter (N=2 cm⁻¹ and N=4 cm⁻¹ designs), the heat transfer rates steadily increase as compared to the bare surface. The performance enhancement reaches a maximum at a Bond number of unity, Bo_(P) ^(1/2)=1, and then decreases for smaller Bond numbers (N≧6 cm⁻¹). As the Bond number decreases, two factors affecting performance arise. First, the pitch between the epoxy divisions becomes smaller than the nominal bubble departure diameter, and secondly, the effect of surface tension becomes more pronounced. For N≧6 cm⁻¹ bubbles grow to diameters wider than the pitch between epoxy divisions before they can depart. This impedes the counter flow of cooler liquid returning to the surface and disrupts the desired spatial ordering of flow fields. Additionally, for Bo_(P)<1 the effects of surface tension on the bubble departure process is evident, where the non-wetted base area beneath a bubble can grow to the entire width of the copper section. This is particularly evident for the N=12 cm⁻¹ design, which has a Bond number of Bo_(P)=0.13, and shows performance worse than bare copper. In this case, the reduction of area available to conduct heat and the adverse effects of surface tension outweigh potential improvements associated with ordered flows. A decrease in HTC and CHF of approximately 25% as compared to a bare copper surface is observed.

By imparting in-plane variations in surface temperature onto flat surfaces using low-conductivity materials, extreme increases in pool boiling heat transfer can be achieved. By tuning the wavelength of these variations to coincide with the capillary length of the fluid, a resonance-like enhancement effect is seen leading to a greater than 5× improvement in heat transfer rate at moderate superheats. The counterintuitive result by which heat transfer is increased with the addition of non-conductive materials is shown to be a product of the resulting flow field near the surface. By using temperature gradients to order the location of nucleation sites, as well as promote the formation of distinct pathways for liquid and vapor flows, HTC has been increased from 41 kW/m²K to 210 kW/m²K (at ΔT=11 K) and CHF has been increased from 116 W/cm² to 230 W/cm².

The principle of tailoring flow fields through variations in local surface temperature represents a novel and potentially transformative tool for the enhancement of boiling heat transfer in next-generation high heat flux applications. Bi-conductive surfaces not only produce substantial increases in performance (>5× increase in HTC shown here), but are also inexpensive to manufacture using traditional methods, scalable to large areas and various material, and do not contain fragile surface structures or thin coatings. As a result they are easily implementable and naturally insensitive to the degradation, mechanical failure, and fouling associated with other boiling enhancement approaches.

The apparatus and methods of the present invention can be adapted for boiling under pressures other than one atmosphere. A change in the pressure during boiling will change the capillary length of the bubble. Surface tension, sigma and the densities of the liquid and vapor all vary as a function of boiling pressure. Thus, it is within the scope of the present invention to adapt the apparatus and methods to boiling at different pressures by taking the pressure into account in the calculation of capillary length λ_(C).

These bi-conductive surfaces promote HTC and CHF by ordering the vapor and liquid flow-fields during pool boiling, resulting in enhanced bubble dynamics and departure, as well as a delay of the boiling crisis. These enhancements are explicitly derived from bulk material properties (thermal conductivity), as opposed to surface properties or surface structures. Unlike surface coatings, this fundamental mechanism is not susceptible to material degradation and long-term reliability issues, nor is it reliant on specific fluids or fluid properties to promote boiling, as is required for surfaces incorporating low surface energy materials. Similarly, these flat, or substantially flat bi-conductive surfaces do not rely on surface wicking nor are they susceptible to mechanical failure or clogging, which may occur on structured surfaces. Additionally, they can be easily fabricated using a variety of materials with traditional machining techniques and do not rely on complex manufacturing, or precise geometric shapes, to impart boiling enhancement. As such, in one embodiment of the present invention, the heat transfer surface does not contain nano-structures.

The present method and apparatus is capable of utilizing materials other than epoxy and copper. Additionally, variations in the dimensions of the surface are also contemplated as part of the present invention even though such variations may not provide the maximum benefit these variations are capable of providing an improvement over materials currently used in the art.

According to an embodiment of the invention, the apparatus defining a heat transfer surface for transfer of heat from the apparatus to a liquid has a bi-conductive surface preferably having a periodic arrangement of low-conductivity material embedded within a high-conductivity substrate. FIGS. 1 and 3 show a bi-conductive surface fabricated according to an embodiment of the invention. Most preferably, the bi-conductive surface contains only two materials. However, the surface may contain as many materials as desired as long as at least some of the materials have suitable differences in thermal conductivities. All materials used to form the heat transfer surface of the apparatus must be capable of withstanding the conditions to which the materials will be subjected during a boiling process, including at least temperature, pressure and load. Preferably, the apparatus is selected from a vessel and an immersion heater.

Suitable high thermal conductivity materials may include, for example, metals, semiconductor materials and carbon-based materials. Exemplary metals include copper, aluminum, silver, titanium and steel. Exemplary semiconductor materials include silicon, silicon carbide, and gallium nitride. Exemplary carbon-based materials include diamond and graphite. Most preferably, the high conductivity material is copper.

Suitable low thermal conductivity materials may include, for example, polymers and ceramics. More particularly, suitable low conductivity materials may include plastic, rubber, epoxies and resins, as well as quartz and glass materials. The low conductivity material is preferably a two-part high conductivity epoxy.

The materials having two different thermal conductivities may be arranged in a predetermined spatial relationship relative to each other. Specifically, the low thermal conductivity material can form lines across the surface of the high thermal conductivity substrate, resulting in each surface portion having a rectangular, or substantially rectangular shape to its cross section. Alternatively, the embedded material can be formed in the shape of dots. The dots can have any shape, and preferably the shape of the cross section of the dots as viewed along the plane of the surface of the substrate is circular, elliptical, rectangular, square, substantially circular, substantially elliptical, substantially rectangular, substantially square, or a combination of two or more of said shapes. A preferred surface portion of the material within the dots has a length of from about 0.01 to about 50 mm in a longest dimension measured along the plane of the surface of the substrate material, more preferably, the length of the dots is from about 0.05 to about 30 mm, or from about 0.1 to about 10 mm, and most preferably from about 2 to about 5 mm in a longest dimension.

The spacing between the surface portions of one of the materials is designed based on the capillary length for a bubble of a predetermined liquid, λ_(C), which is defined in detail above. Preferably, the spacing between surface portions of one material is from about 0.1λ_(C) to about 10λ_(C), more preferably, 0.2λ_(C) to about 5λ_(C), or from about 0.3λ_(C) to about 3λ_(C). Even more preferably the spacing between surface portions of one material is from about 0.5λ_(C) to about 2λ_(C), and most preferably, the distance between surface portions of one of said materials is about λ_(C). In a preferred embodiment the defined spacing is between surface portions of the low thermal conductivity material.

Although the dots, or the more determinant shape, have been described as being formed by the material having the lowest thermal conductivity, the more determinant shape may also be formed by the material having the highest thermal conductivity. The material having the lowest of the thermal conductivities preferably forms from about 1-60% of the heat transfer surface of the apparatus, more preferably from about 2-50%, or about 4-30%. Even more preferably, the material having the lowest of the thermal conductivities preferably forms from about 8-25%, about 12-22%, or about 16-20% of the heat transfer surface of the apparatus. Most preferably the material with the lowest thermal conductivity forms about 18% of the heat transfer surface of the apparatus.

The thermal conductivity of the low-conductivity material is several orders of magnitude less than that of high conductivity substrate. Preferably, the two different materials have a ratio of thermal conductivities of the high conductivity material to the low conductivity material of greater than about 10:1, or greater than about 50:1. More preferably the ratio of thermal conductivities is greater than about 100:1, 200:1 or 300:1. Most preferably, the ratio of thermal conductivities of the high conductivity material to the low conductivity material is greater than 400:1.

The apparatus can use materials having any thermal conductivity, but preferably, the thermal conductivity of each material forming the apparatus surface is from about 0.01-100 W/mK, or about 0.1-900 W/mK, or about 1-500 W/mk. Most preferably, the thermal conductivities of the materials are about 2-450 W/mK. Most preferably, as included above, the low conductivity material is epoxy (<1 W/mK) and the high conductivity material is copper (˜400 W/mK).

In a preferred method of creating the bi-conductive surface, grooves are machined into suitable high thermal conductivity material substrate. The grooves may be formed in any shape desired for the insertion of the low-conductivity material. The grooves can be machined into the substrate material by any process that is known to one skilled in the art, for example, wire electrical discharge machining (EDM) can be used. In an optional step to promote adhesion of the low-conductivity material, the high-conductivity substrate can be treated with an alkaline solution to produce an oxide layer with nano-surface roughness. The grooves are then subsequently filled with a suitable low conductivity material. The low-conductivity material is then cured to achieve a good bond.

After curing the entire surface is abraded to remove excess low-conductivity material. The abrading step results in flat surfaces with lines of low conductively material dividing the high conductivity material into parallel strips. The final product is then cleaned and dried using any suitable method known in the art. Preferably, the cleaning and drying step is accomplished using solvents and gas flow, such as with N₂.

The apparatus discussed above can be used in a method of boiling at least one liquid to provide increased heat transfer from a heat transfer surface of the apparatus to a liquid by boiling the liquid in contact with the apparatus. The critical heat flux from a heat transfer surface can also be increased by using the apparatus described above. Additionally, an embodiment of the present invention can be used to tune a heat transfer surface of an apparatus by forming the heat transfer surface using at least two different materials having different thermal conductivities arranged in a predetermined spatial relationship which is configured to further increase the critical heat flux from the heat transfer surface to a liquid by providing a spacing between the materials that is related to a capillary length of a bubble of a predetermined liquid. Preferably, the spacing between surface portions of one material is from about 0.1λ_(C) to about 10λ_(C), more preferably, from about 0.2λ_(C) to about 5λ_(C), or from about 0.3λ_(C) to about 3λ_(C). Even more preferably the spacing between surface portions of one material is at from about 0.5λ_(C) to about 2λ_(C), and most preferably, the distance between surface portions of one of said material is about λ_(C)

The following examples have been presented for the purpose of illustration and description and are not to be construed as limiting the scope of the invention in any way. The scope of the invention is to be determined from the claims appended hereto.

Example 1 Bi-Conductive Surface Fabrication

Bi-conductive surfaces were fabricated by embedding lines of a low-conductivity epoxy into a copper substrate. Copper sheets (1 mm thickness) were cut to size and grooves were machined into them using Wire Electrical Discharge Machining (EDM). The EDM wire thickness was 0.254 mm with a reported minimum spark gap of 0.381 mm±0.127 mm. The copper was then treated with an alkaline solution to produce an oxide layer with nanoscale surface roughness to promote adhesion between the copper and epoxy. The surfaces were then coated with a non-conductive high-temperature two-part epoxy (Aremco™ 526N) filling all of the grooves. The epoxy was cured at 93° C. for 2 hours, followed by 163° C. for 12 hours to achieve a maximum strength bond. After curing, the surfaces were manually sanded with 200 grit sandpaper until the bare copper between each epoxy division was exposed. The bare copper surfaces (with no epoxy divisions) were also sanded using the same method. The surfaces were finally cleaned with solvents and dried with N₂.

Bi-conductive surfaces were fabricated with a varying number of epoxy divisions per centimeter, N. FIG. 1a shows optical images of the N=2 cm⁻¹ and N=12 cm⁻¹ designs. In total, seven distinct surfaces were fabricated and tested including a bare copper surface and bi-conductive surfaces with N=2, 4, 6, 8, 10, and 12 cm⁻¹. FIG. 3 shows scanning electron microscope (SEM) images of the embedded epoxy divisions which have a measured width of 420±5 μm, depth of 290±23 μm, and center-to-center pitches of P=0.96−3.7 mm.

Example 2

Evaluating equation S8 using the experimentally measured heat transfer coefficients during nucleate boiling, h=50-210 kW/m²K (FIG. 3), results in q_(E)/q_(T)=0.2%-2% for the highest performing surfaces (P=3.7-1.8 mm). For the lower performing surfaces (P=1.39-0.96 mm) this increases to q_(E)/q_(T)=0.8%-5%. Similarly, by evaluating equation S10 it can be shown that the ratio of the superheats between the epoxy and fluid to the copper and fluid is ΔT_(sat,E)/ΔT_(sat,C)=1.9%-6.7%, over the same range of h.

Prior to the onset of nucleate boiling, the measured heat transfer coefficients reach values of h˜5 kW/m²K. During this convection-dominated region, the lower heat transfer coefficients result in higher convective resistances that become comparable to the conductive resistances in the epoxy. Because of this, the percentage of heat transfer over the epoxy increases to q_(E)/q_(T)=5%-11% for the highest performing surfaces (P=3.7-1.8 mm), and q_(E)/q_(T)=15%-24% for the lower performing surfaces (P=1.39-0.96 mm), with ΔT_(sat,E)/ΔT_(sat,C)=41%. This ˜60% reduction in wall superheat over the epoxy divisions is sufficient to produce unstable convective flows and promote the preferential nucleation of vapor bubbles near the center of the copper segments.

Example 3 Pool Boiling Characterization and Imaging

Surfaces were characterized using a custom-built test set-up as previously reported by Rahman et al. See, Rahman, M. M., Ölçero{hacek over (g)}lu, E. & McCarthy, M. Role of Wickability on the Critical Heat Flux of Structured Superhydrophilic Surfaces. Langmuir 30, 11225-11234 (2014) and Rahman, M. M., Ölçero{hacek over (g)}lu, E. & McCarthy, M. Scalable Nanomanufacturing of Virus-templated Coatings for Enhanced Boiling. Advanced Materials Interfaces 1, 1300107 (2014). The setup consists of a copper heater block with PTFE insulation embedded with two cartridge heaters allowing for a maximum power of 1,000 W. Five T-type thermocouples were inserted into the copper block equally spaced 6 mm apart with the topmost thermocouple located directly beneath the sample.

The temperature measurements were recorded using NI DAQ system, where the average heat flux in the copper block was calculated using Fourier's conduction law. The sample surface temperature was calculated by considering all of the relevant thermal resistances between the surface and the topmost thermocouple, as described. A polycarbonate chamber was used to house the water bath; with an immersion heater and thermocouple probe maintaining saturated conditions and atmospheric pressure. Degassed, deionized water was used as the working fluid, and all tests were carried out up to CHF. Visualization of the boiling process was conducted at low heat fluxes using a Phantom V210 high-speed camera (Vision Research) recording at 1,000 fps. The surfaces were initially maintained at saturated condition for 1 hour after which a small increment of heat flux (2 W/cm² to 5 W/cm²) was applied to the surfaces until nucleation was observed. Heat flux was further increased up to 20 W/cm² until the visibility of bubble dynamics becomes difficult.

Each of the fabricated surfaces has been characterized during pool boiling of saturated water at atmospheric conditions using a custom built experimental apparatus. The complete details of the apparatus, testing procedures, and experimental uncertainty can be found in prior publications. See, Rahman, M. M., Ölçero{hacek over (g)}lu, E. & McCarthy, M. Role of Wickability on the Critical Heat Flux of Structured Superhydrophilic Surfaces. Langmuir 30, 11225-11234 (2014) and Rahman, M. M., Ölçero{hacek over (g)}lu, E. & McCarthy, M. Scalable Nanomanufacturing of Virus-templated Coatings for Enhanced Boiling. Advanced Materials Interfaces 1, 1300107 (2014). Briefly, each surface was soldered to an insulated copper heater block and submerged in a bath of saturated water. The heat flux delivered to the surface, q″, is periodically increased in small increments and the system is left to reach thermal equilibrium, typically at about 10-20 minutes. After this the surface temperature and heat flux are recorded, and the process is repeated until the CHF is reached. CHF is taken as the highest stable heat flux prior to the uncontrollable increase in surface temperature associated with dry-out. The average wall temperature at the surface of the sample, T _(w), is measured using a thermocouple placed at the top of the heater block, and accounts for the various thermal resistances between this thermocouple and the surface. These include the resistances across the solder interface and bulk copper, as well as the resistance across the composite copper-epoxy region near the surface of the sample. While the embedded epoxy produces in-plane temperature variations on the surface, it does not greatly impact the overall thermal resistance of the sample itself. For the extremely thin samples that were tested (1 mm thickness), the increase in overall thermal resistance of the substrate was ˜6% for the N=4 cm⁻¹ design. For a more realistic wall thickness of ¼ inch (6.35 mm), the increase in thermal resistance associated with adding embedded epoxy divisions drops to less than 1%.

During each test the average wall superheat, ΔT, is measured where

ΔT=T _(w) −T _(sat)  (7)

and the associated heat transfer coefficient (HTC) is calculated as

$\begin{matrix} {{H\; T\; C} = {\frac{q^{''}}{\Delta \; T}.}} & (8) \end{matrix}$

Additionally, visualization of the boiling process is conducted using a Phantom V210 high-speed camera (Vision Research) recording at over 3,000 fps. High-speed imaging is used to visualize bubble dynamics during nucleate boiling at low heat fluxes. At higher fluxes the large production of vapor makes visualization difficult, resulting in no useful information regarding the impact of bi-conductive surface on the boiling process.

FIG. 10 shows representative images extracted from high-speed imaging, showing nucleate boiling on bi-conductive surfaces with various values of N. All of the surfaces tested exhibited similar incipience temperatures, with the onset of nucleate boiling occurring around ΔT of ˜5-7 K. It can be seen that bubbles form exclusively on the copper regions, with the low-temperature epoxy divisions suppressing the nucleation process as expected. More importantly, the epoxy divisions remain wetted at all times and resist the lateral motion of bubbles across them. This allows for the formation of ordered pathways for liquid return above the cold epoxy divisions.

FIG. 8 shows the measured boiling curves, and heat transfer coefficient as a function of superheat for each surface that was tested. The bare copper surface reached a CHF of ˜116 W/cm² with a maximum HTC of ˜70 kW/m²K. Substantial increases in boiling performance can be seen for nearly all of the bi-conductive surfaces as compared to bare copper. At moderate superheats (ΔT=10-11 K), an increase in heat flux and heat transfer coefficient of greater than 5× has been demonstrated using bi-conductive surfaces with a pitch of P=2.33 mm (N=4 cm⁻¹). While the incipience temperature did not vary substantially for any of the tested surfaces, heat transfer was increased due to enhanced bubble dynamics on the bi-conductive surfaces. This demonstrates that the addition of epoxy does not enhance HTC by promoting nucleation at lower superheats, as shown for structured surfaces and surfaces with mixed wettability.

By creating in-plane variations in the superheat temperature, the nucleation, growth, and departure of vapor has been substantially affected. Spatial ordering of the flow field allows for the efficient removal of vapor and return of liquid, accelerating the ebullition cycle and promoting the departure of bubbles. The efficient return of replenishing liquid has been seen to delay dry-out and enhance CHF up to a factor of 2× using bi-conductive surfaces. While no formal characterization of the long-term reliability of the samples has been conducted, none of the bi-conductive surfaces tested in this work have shown any mechanical failure or degradation during several hours of testing.

Example 4

The pool boiling experimental apparatus used in this example and its measurement capabilities and uncertainties have been reported in previous publications. See, Rahman, M. M., Ölçero{hacek over (g)}lu, E., and McCarthy, M., Role of Wickability on the Critical Heat Flux of Structured Superhydrophilic Surfaces, Langmuir, vol. 30, no. 37, pp. 11225-11234, 2014; Rahman, M. M., Ölçero{hacek over (g)}lu, E., and McCarthy, M., Scalable Nanomanufacturing of Virus-templated Coatings for Enhanced Boiling, Advanced Materials Interfaces, vol. 1, no. 2, 1300107, 2014; and Rahman, M. M., Pollack, J., and McCarthy, M., Increasing Boiling Heat Transfer using Low Conductivity Materials, Scientific Reports, vol. 5, 13145, 2015. The setup, as shown in FIGS. 11A and 11B, consisted of a copper heater block with two embedded 500 W cartridge heaters controlled using a variable autotransformer. The heater assembly was insulated on all sides with thick PTFE insulation and five T-type thermocouples are inserted into the copper at an equal spacing to measure the steady state heat flux. The samples were soldered to the copper and a thermocouple was embedded immediately underneath the surface to determine the samples' surface temperatures during boiling, accounting for all of the relevant thermal resistances. A polycarbonate housing containing degassed, deionized water was used as the boiling chamber, with an auxiliary cartridge heater used to maintain the bath at saturation conditions and ambient pressure. A T-type thermocouple was used to continuously monitor the saturation temperature of the bath, and all temperatures and heat flux measurements were recorded using a National Instruments data acquisition system. Deionized water was degassed by boiling at 100° C. for 30 minutes, prior to being placed in the chamber.

The heat flux was then slowly increased until a surface temperature of 100° C. is reached, and the heat flux is then maintained at that level for 30 minutes. To begin testing, the heat input to the sample was increased in small increments and the system was allowed to reach thermal equilibrium. All measurements were recorded after the temperature variations for each thermocouple became less than 0.5° C. for 20 minutes. Each sample was tested up to CHF, which was taken as the largest stable heat flux attainable. Beyond CHF a rapid increase in surface temperature was observed, resulting in the sample de-soldering from the copper block.

The experimental uncertainties associated with the measured quantities have been calculated and reported in an earlier work. See, Rahman, M. M., Ölçero{hacek over (g)}lu, E., and McCarthy, M., Scalable Nanomanufacturing of Virus-templated Coatings for Enhanced Boiling, Advanced Materials Interfaces, vol. 1, no. 2, 1300107, 2014. For the boiling apparatus used in this study, the estimated uncertainties in the heat flux, wall superheat, and heat transfer coefficient were found to be ±5.95 W/cm², ±1.75 K, and ±3.58 kW/m²K, respectively. FIG. 11B shows a schematic representation of the experimental setup used to characterize surface wicking. It consisted of a perfluoroalkoxy capillary tube filled with deionized water, a translational stage to raise the surface into contact with the pendant droplet, and a high speed camera to capture the change in meniscus height during wicking.

Comparative Example 1—Nanostructured Surfaces and Wickability

Nanostructured coatings for boiling enhancement have been studied extensively.

Specifically, silicon and copper nanowires on silicon surfaces have been used to increase CHF. Numerous other researchers have investigated the impact of nanostructures on boiling and have offered a variety of explanations. Most notably the role of surface wicking has been cited as a critical factor for CHF enhancement. Nanostructured hydrophilic coatings produce superhydrophilic surfaces with contact angles approaching zero degrees. These structures can also wick liquids laterally across a surface during boiling, which is seen as a viable mechanistic explanation of the delayed dry-out and increased CHF observed for nanostructured surfaces.

To demonstrate the effects of nanoscale coatings on boiling heat transfer, copper substrates have been oxidized to create high-surface-area copper oxide (CuO) nanostructures. The sharp blade-like CuO nanostructures were fabricated using the method described by Chu et al., where a copper substrate is immersed in a mixture of NaClO₂, NaOH, Na₃PO₄.12H₂O, and deionized water (3.75:5:10:100 wt %) at 96° C. for 10 minutes. See, Chu, K.-H., Joung, Y. S., Enright, R., Buie, C. R., Wang, E. N., Hierarchically Structured Surfaces for Boiling Critical Heat Flux Enhancement, Applied Physics Letters, vol. 102, no. 15, 151602, 2013.

FIG. 12A shows scanning electron microscope (SEM) images of the fabricated CuO nanostructured surfaces at two different magnifications. FIGS. 12B and 12C show heat flux as a function of wall superheat, and heat transfer coefficient as a function of heat flux for the nanostructured surface as compared to bare copper. The horizontal arrows indicate CHF for each surface, which corresponds to the largest stable heat flux before dry-out. It can be seen that the bare Cu reaches a CHF value of about 117 W/cm² with a maximum HTC of 70 kW/m²K. A CHF value of 196 W/cm² was measured for the nanostructured CuO surface at a wall superheat of 34.5 K. The experimental uncertainties for CHF and maximum HTC are ±3.0% and ±6.3%, respectively. This performance is repeatable and closely matches the results of several researchers for nanostructured boiling.

As can be seen, the addition of nanostructures results in a notable increase in CHF, but also a simultaneous decrease in HTC over the entire boiling curve. CHF has been increased by 68%, and the maximum HTC has been reduced by 19%. This decrease in HTC is attributed to the suppression of active nucleation sites due to the nanostructured coating. The CuO nanostructures reduce the effective cavity size of a range of potential nucleation sites on the machined copper surface to much less than 1 μm, thus requiring larger superheats to activate them. Conversely, several researchers have shown increases in HTC with the addition of nanostructures for boiling on silicon substrates. This is due to the fact that the sizes of potential nucleation sites on a polished silicon surface are much smaller than the size of the cavities created by typical nanostructured coatings.

The increase in CHF seen in FIG. 12B is explained by evaluating the ability of the nanostructured coating to laterally wick liquids across its surface. Rahman et al. has previously reported a semi-empirical CHF correlation based on surface wickability. See, Rahman, M. M., Ölçero{hacek over (g)}lu, E., and McCarthy, M., Role of Wickability on the Critical Heat Flux of Structured Superhydrophilic Surfaces, Langmuir, vol. 30, no. 37, pp. 11225-11234, 2014. The model was experimentally validated showing excellent agreement for surfaces with micro, nano, and hierarchical structures. Additionally, it was shown to be independent of structure material, morphology, and substrate material, as well as being insensitive to the effects of surface damage and fouling. The predicted CHF value relative to Zuber's approximation (q″_(CHF, Z)) is given as:

q″ _(CHF) =q″ _(CHF,Z)(1+Wi)  (9)

where the dimensionless wicking number, Wi, is defined as:

$\begin{matrix} {{Wi} \equiv \frac{{\overset{.}{V}}_{0}^{''}\rho_{l}}{{\rho_{v}^{1/2}\left\lbrack {\sigma \; {g\left( {\rho_{l} - \rho_{v}} \right)}} \right\rbrack}^{1/4}}} & (10) \end{matrix}$

and is evaluated using fluid properties at saturation conditions. The wicking number, Wi, is the non-dimensional form of the maximum wicked volume flux, {dot over (V)}″₀, and represents the ratio of the liquid mass flux wicked into the surface structures relative to the critical mass flux of vapor leaving the surface as calculated using hydrodynamic analysis. The maximum wicked volume flux is calculated as:

$\begin{matrix} {{\overset{.}{V}}_{0}^{''} = {\frac{1}{A_{W}}\left( {{dV}/{dt}} \right)_{t = 0}}} & (11) \end{matrix}$

using the experimental technique shown in FIGS. 13A-13A.

A perfluoroalkoxy tube of 500 μm inner diameter was filled with about 1.5 μL of deionized water using a micro-syringe pump. The tube was mounted vertically with a pendant droplet forming at the lower end. A structured sample to be tested was slowly raised up from below the tube with a translational stage with micron-level precision. When the pendant droplet touched the sample the liquid was wicked into the surface structures and propagated radially outward from the point of contact. After the initial contact, two phenomena occur sequentially as shown in FIG. 13A for the CuO nanostructured surfaces. First, the pendant droplet deforms to wet the surface and spreads out to a constant wetted area, A_(W), over approximately the first 5 ms. After this initial spreading phase ends, the liquid was then wicked through the surface structures and the liquid flow rate was measured by monitoring the change in height of the liquid meniscus within the tube. As seen, this technique successfully segregated these two phases to allow for the direct measurement of wicking after all spreading had ceased.

A high speed camera was used to capture the motion of both the pendant droplet spreading, as well as the dropping meniscus in the tube, at a frame rate of 1000 Hz. FIG. 13B shows results from image tracking of the meniscus height, where the dynamic wicked volume was calculated as V=A_(T)h. Here, A_(T) is the inner cross-sectional tube area and h is the displacement of the meniscus. Similarly, FIG. 13C shows the measured wetted area, A_(W), as a function of time. The insets in both graphs show that the initial moment of contact, where t=0 is set to coincide with the moment wicking begins. As can been seen, spreading occurred prior to wicking (t<0) and the resulting maximum volumetric flow rate and wetted area can be determined at t=0. The uncertainty in wetted radius and meniscus height was estimated using an image pixel size of ±0.014 mm, resulting in an uncertainty in wicked volume flux (based on propagation of measurement error) of ±0.16 mm/s.

Using the measured values for the CuO nanostructured surfaces, the wicked volume flux was {dot over (V)}″₀=2.78 mm/s with an experimental uncertainty of ±5.8%, resulting in a dimensionless wicking number of Wi=0.73. Rahman's CHF correlation (Eq. 1) therefore predicts a CHF value of q″_(CHF)=192 W/cm², as compared to the measured value of q″_(CHF)=196 W/cm². This represents a discrepancy between prediction and measurement of about 2%, which is less than the estimated accuracy of the experimental apparatus, demonstrating the efficacy of this model.

The addition of nanostructured coatings onto copper surfaces was shown to increase CHF and delay dry-out via wicking, but also decrease HTC by suppressing nucleation. This highlights the complexities of boiling and the difficulty in engineering surfaces for boiling enhancement. CHF represents the maximum heat transfer rate and essentially limits the operating range of a boiling surface. Most systems, however, do not operate near CHF for safety reasons. HTC is arguably a more important measure of boiling enhancement and, as was shown, nanostructured coatings degrade HTC on copper.

Comparative Example 2—Mixed Wettability and Nucleation

HTC is a measure of the efficiency of boiling and strongly depends on the nucleation process, the nucleation site density, and the bubble ebullition cycle. One reported method of increasing HTC during boiling is by increasing the activation of nucleation sites at low wall superheats using surfaces low-surface-energy materials. The inclusion of hydrophobic spots onto an otherwise hydrophilic surface was shown by Betz et al. See, Betz, A. R., Xu, J., Qiu, H., and Attinger, D., Do Surfaces with Mixed Hydrophilic and Hydrophobic Areas Enhance Pool Boiling?, Applied Physics Letters, vol. 97, no. 14, 141909, 2010. By reducing the wall superheat required to activate the engineered nucleation sites using hydrophobic dots, an HTC enhancement of 100% was reported for these patterned biphilic surfaces. By further decreasing the wettability of the nucleation sites Betz et al. increased this HTC enhancement up to 650% using nanostructured superbiphilic surfaces.

The effect of mixed-wettability on nanostructured surfaces during pool boiling was demonstrated using nanostructured nickel coatings on silicon substrates. FIG. 14A shows SEM images of the nickel nanostructures, both with and without a thin conformal PTFE coating, as well as a schematic representation of the mixed-wettability pattern tested. Biotemplated nickel nanostructures are fabricated through the self-assembly and metallization of the Tobacco mosaic virus (TMV) using a simple room-temperature solution-based nanofabrication technique as reported in previous publications. See, Rahman, M. M., Ölçero{hacek over (g)}lu, E., and McCarthy, M., Scalable Nanomanufacturing of Virus-templated Coatings for Enhanced Boiling, Advanced Materials Interfaces, vol. 1, no. 2, 1300107, 2014; and Ölçero{hacek over (g)}lu, E., Hsieh, C.-Y., Rahman, M. M., Lau, K. K. S., and McCarthy, M., Full-Field Dynamic Characterization of Superhydrophobic Condensation on Biotemplated Nanostructured Surfaces, Langmuir, vol. 30, no. 25, pp. 7556-7566, 2014.

Briefly, gold-coated silicon substrates were immersed in a phosphate buffer solution containing purified TMV for 24 hours during which the viruses assemble onto the surface. The viral nano-rods were then metallized using a palladium-activated autocatalytic nickel solution. This results in a rough superhydrophilic nanostructured nickel surface with average nanostructure heights of 1-1.5 μm and diameters of about 100 nm. The nanostructured surfaces were then patterned using traditional photolithography to create a photoresist layer with 45 μm diameter openings spaced 90 μm apart. A thin coating of PTFE (AF1600 Teflon) was then spin-coated, cured, and lifted off of the nanostructures, resulting in superhydrophobic islands on an otherwise superhydrophilic nanostructured surface (FIG. 14B).

FIGS. 14B and 14C show the boiling curves for the nanostructured biphilic surface as compared to a TMV-templated nickel nanostructured surface with no PTFE islands. The nanostructured surface reached a CHF of 196 W/cm² with an experimental uncertainty of ±3.0%, with the ONB occurring at a wall superheat of 6 K. The nanostructured biphilic surface has an ONB at a wall superheat of less than 3 K, and reaches a CHF value of 151 W/cm² with an experimental uncertainty of ±3.9%. The maximum HTC for the nanostructured biphilic surfaces is 149 kW/m²K, with an experimental uncertainty of ±2.4%, representing a 116% increase over the superhydrophilic nanostructured surfaces without mixed wettability. While HTC has been enhanced by promoting the activation of nucleation sites at lower superheats, the CHF for nanostructured biphilic surfaces has been reduced by about 25% as compared to nanostructured surfaces. This reduction in CHF is attributed to an effective reduction in capillary wicking. The addition of superhydrophobic islands in the arrangement shown in FIG. 14A will reduce the ability of liquid to be wicked laterally across the surface by creating barriers that liquid cannot pass through. This again demonstrates the complex and coupled nature of boiling phenomena and engineered surface designs to simultaneously increase CHF and HTC.

Experimental 1—Bi-Conductive Surfaces and Bubble Dynamics

The enhancement mechanisms characterized in the prior two sections occur primarily at the “beginning” of the boiling curve (ONB), and the “end” of the boiling curve (CHF). By enhancing bubble dynamics and the ebullition cycle, boiling performance can be increased across the entire boiling curve. The enhancements in CHF and HTC using nanostructures and mixed-wettability rely on surface and interfacial phenomena, namely surface capillary wicking and the nucleation process. The bi-conductive surfaces according to the present invention consist of flat copper substrates with embedded epoxy divisions as shown in FIGS. 15A-15C. Copper surfaces are machined to create an array of 420 μm wide, 290 μm deep channels using Wire EDM (Electrical Discharge Machining). The surfaces are then filled with a two-part high-temperature epoxy (Aremco-Bond™ 526-N) and cured in a convection oven initially at 93° C. for 2 hours and later at 163° C. for 4 hours. After curing, the surfaces are manually sanded with a 200 grit sand paper resulting in flat surfaces with an array of rectangular copper sections separated by embedded epoxy divisions. By embedding a low-conductivity epoxy into a high-conductivity copper surface in a periodic arrangement, spatial variations in surface temperature are generated when the surface is heated. During boiling the epoxy divisions remain cool (nearly equal to the fluid saturation temperature), and therefore suppress nucleation and remain wetted at all times. As the surface is initially heated the liquid above the heated copper gets warmer and is replaced by the cold liquid from the epoxy divisions due to natural convection. This creates a stagnation point at the center of the copper sections. By imparting a local maximum in surface temperature, the bi-conductive design promotes preferential nucleation near the center of the copper regions. As bubbles form and depart from above the copper, replenishing liquid returns to the surface from above the cooler epoxy divisions. This results in an ordered liquid and vapor flow field during boiling, as schematically shown in FIG. 15D.

FIGS. 16A-16B show the pool boiling performance of the optimal bi-conductive design, with a pitch between epoxy divisions of P=2.33 mm (as seen in FIG. 15C), compared to a bare copper surface. Heat flux as a function of wall superheat is plotted in FIG. 16A and heat transfer coefficient as a function of heat flux is plotted in FIG. 16B. The heat flux and HTC across the bi-conductive surface were calculated using the total surface area in contact with the fluid, including both the copper and epoxy regions. The bi-conductive surface reached a CHF of 230 W/cm², representing about a two-fold increase in CHF and a three-fold increase in maximum HTC. The experimental uncertainties for CHF and maximum HTC for the bi-conductive surface are estimated to be ±2.6% and ±1.7%, respectively.

At a moderate wall superheat of about 10 K, the bi-conductive surfaces show a five-fold increase in heat flux as compared to bare copper. These enhancements are derived directly from enhanced bubble dynamics and an increase in the ebullition cycle. CHF is increased without the use of surface structures or capillary wicking, and HTC is increased without using low-surface-energy materials and with no change in ONB.

Experimental 2—Bi-Conductive Heterogenous Surfaces

Nanostructures have been shown to increase CHF through capillary wicking, but degrade HTC. Mixed wettability has been shown to increase HTC by increasing nucleation sites and triggering ONB at lower superheats, but degrades CHF. The bi-conductive surfaces, however, have been shown to simultaneously increase CHF as well as HTC across the entire boiling curve. They have a higher CHF than nanostructured coatings, and a higher HTC as compared to biphilic surfaces. Most importantly, the mechanisms of enhancement for the bi-conductive surfaces (bubble dynamics and spatial order) are independent of those for nanostructured coatings (capillary wicking) and surfaces with mixed wettability (nucleation). This suggests that these different enhancement approaches can be superimposed onto one another for further increases in performance.

FIGS. 17A and 17B show the two heterogeneous surface designs fabricated and characterized here. Nanostructured bi-conductive copper surfaces (FIG. 17A) were fabricated by using the previously described CuO nanostructure growth technique applied directly to an optimized bi-conductive surface (P=2.33 mm). Nanostructured bi-conductive biphilic surfaces (FIG. 17B) were also fabricated by using the previously described technique to create mixed wettability on nanostructured surfaces. Nanostructured bi-conductive surfaces were patterned using photolithography, after which PTFE was spun on, cured, and finally lifted-off to yield the pattern shown in FIG. 17B. FIG. 17C shows SEM images of a nanostructured bi-conductive biphilic surface, where an approximately 50 μm thick line of PTFE-coated nanostructures was patterned at the center of the nanostructured CuO region. FIG. 17D shows a magnified image of the boundary between superhydrophilic CuO nanostructures and the superhydrophobic PTFE nanostructures.

FIG. 17E shows a schematic representation of the desired flow field during nucleate boiling on the nanostructured bi-conductive biphilic surfaces. Nucleation is promoted at low superheats on the superhydrophobic PTFE nanostructures, and suppressed on the epoxy divisions due to a locally low surface temperature. By selectively promoting and suppressing nucleation, spatial order of the resulting liquid and vapor flow paths was created to enhance the ebullition cycle increasing both CHF and HTC. The nanostructures on the copper surface provided a pathway to wicked liquid from the epoxy divisions to the superhydrophobic nucleation sites, thus further delaying dry-out.

The performance of both heterogeneous designs (FIGS. 17A and 17B) is shown in FIGS. 18A and 18B compared against bare copper, nanostructured surfaces, and bi-conductive surfaces, where the total projected footprint area (copper and epoxy) is used to calculate heat flux and HTC for all surfaces. As can been seen, the bi-conductive surfaces notably outperform the nanostructured surfaces in both CHF (17% higher) and HTC (270% higher). Over the majority of the boiling curve, the nanostructured bi-conductive surfaces, denoted by open circles in FIGS. 18A and 18B, show comparable performance to the bi-conductive surfaces with no nanostructures (open squares). The two curves generally follow one another with the nanostructured bi-conductive surface showing only a modest enhancement in HTC. However, the addition of nanostructures to a bi-conductive surface delayed dry-out and led to an increase in CHF of up to 307 W/cm² with an experimental uncertainty of ±1.9%. This increase in CHF due to capillary wicking through the nanostructures (˜77 W/cm²) is consistent with the increase in CHF observed when adding nanostructures to a bare copper surface (˜79 W/cm²), as seen in FIGS. 12A-12C. Comparing the nanostructured bi-conductive surfaces (open circles) to the nanostructured surfaces (open triangles) highlights the impact of the addition of the epoxy divisions. The two curves show drastically different behaviors, with the addition of bi-conductivity leading to a larger CHF, as well as a substantially increased HTC (>330%). The nanostructured bi-conductive biphilic surfaces (open diamonds) were made by adding mixed-wettability to the nanostructured bi-conductive surfaces (open circles). These PTFE coatings were shown to lower the superheat required for ONB and enhance nucleation, leading to a maximum HTC of 747 kW/m²K which represents a >200% increase when compared to the nanostructured bi-conductive surfaces with no PTFE. As seen before, however, the introduction of superhydrophobic nanostructures limits capillary wicking, resulting in a slight decrease in CHF (19%). The observed increase in HTC is achieved by reducing the wall superheat at high heat fluxes. As seen in FIG. 18A, soon after ONB the required wall superheat decreases from ˜7 K to ˜3 K as heat flux is increased to CHF. This counterintuitive behavior is attributed to the continued and rapid activation of additional nucleation sites at higher heat fluxes, as well as favorable bubble dynamics associated with spatial ordering of liquid vapor and flow fields.

Example 5 Fouling and Degradation of Surfaces During Enhanced Boiling

The purpose of this Example is to investigate the role of suspended contaminants and fouling of engineered surfaces during boiling. In most studies on engineered surfaces for boiling enhancement pure de-ionized water is used as the working fluid. However, many boiling applications use low-purity water that includes various contaminants including, for example, suspended particles, impurities, and contaminants; fouling (e.g. NaCl, MgSO₄, CaSO₄, SiO₂); and salts (e.g MgCl₂, CaCO₃).

This example used inert SiO₂ particles having sizes ranging from 7 nm to 10 μm, and tested bare copper, nanostructured surfaces, and bi-conductive surfaces made according to an embodiment of the present invention.

A copper oxide nanostructured surface was created according to the procedure described above in Comparative Example 1 of Example 4. FIG. 19 shows the nanostructured surface at two different magnifications.

The bi-conductive surfaces were made according to the procedure described above in Experimental Example 1 of Example 4. The pitch was equal to 2.33 mm. FIG. 1A shows the bi-conductive surface that was used in this experiment. Four difference fluids were tested, deionized water, deionized water with 7 nm (0.2 vol. %) SiO₂ particles, deionized water with 100-300 nm (0.2 vol. %) SiO₂ particles, and deionized water with 0.5-10 μm (0.2 vol. %) SiO₂ particles.

The apparatus that was used is shown in FIG. 20. One-dimensional heat conduction though a copper block was used to heat the sample. A constant bath temperature was maintained and degassed and deionized water containing the different sized particles was used. The tests were conducted under saturated boiling at atmospheric conditions. All surfaces were tested to CHF.

The results of the test are shown in FIGS. 21 through 26. FIG. 25 shows all of the results for bare copper. For bare copper, particles deposited on the bare copper surface and formed a porous layer. Heat transfer increased due to wicking through the porous structures, which is consistent with nano fluid boiling as described in the literature. CHF was increased in a similar manner for all nanoparticle sizes. The smallest sized particles showed minimum HTC at CHF, and the largest sized particles demonstrated the highest HTC at CHF.

FIG. 26 shows all of the results for CuO nanostructures. Performance of CuO nanostructures was worse than the performance of the bare copper for all particle sizes and was dependent on the size of the particles. The CHF was relatively consistent for all fluids considered, and the HTC varied with particle size. The nanostructured surfaces degraded HTC by up to 33% and CHF by up to 12% as compared with bare copper surfaces. No enhancement was seen for any conditions containing particles. The worst performance was seen with 200 nm particles and was attributed to clogging of the nanostructures. The effective “pore size” of the nanostructures was on the order of 100s of nanometers. As such, particles larger than the effective “pore size” cannot fit in the “pores” of the structures and have less fouling effect. FIG. 27 shows the fouling of the nanostructured surface after boiling with the 200 nm particles as compared to the surface before boiling.

The performance of the bi-conductive surface was better than that of the bare copper for all fluids and was independent of the size of the particles. The bi-conductive surfaces were found to enhance the HTC by up to 55% and CHF by up to 36% as compared with bare copper surfaces during boiling with particles. The addition of particles did degrade the performance of the bi-conductive surfaces compared to using DI water, but this degradation was independent of the particle size. The size-independent degradation was attributed to an insulating effect caused by the deposition of particles on the surface. The insulating layer reduces the amplitude of temperature variations across the surface. The bi-conductive surface also had the benefit that there was no clogging of surface structures.

Including particle contaminants in the working fluid reduces the performance of both the nanostructures and the bi-conductive surfaces. However, the bi-conductive surfaces still showed significant enhancements relative to the bare copper.

The foregoing examples have been presented for the purpose of illustration and description and are not to be construed as limiting the scope of the invention in any way. The scope of the invention is to be determined from the claims appended hereto. 

What is claimed is:
 1. An apparatus having a heat transfer surface for transfer of heat from the apparatus to a liquid, said heat transfer surface comprising at least two different materials and wherein at least two of said materials have a ratio of thermal conductivities of greater than about 10:1, and the material having the lowest of said thermal conductivities forms from about 1-60% of said heat transfer surface.
 2. The apparatus as claimed in claim 1, wherein at least two of said different materials have a ratio of thermal conductivities of greater than about 100:1.
 3. The apparatus as claimed in claim 1, wherein the material having the lowest of said thermal conductivities forms from about 8-25%, of said heat transfer surface.
 4. The apparatus as claimed in claim 1, wherein said heat transfer surface is formed by only two said materials.
 5. The apparatus as claimed in claim 1 wherein the heat transfer surface is a flat or substantially flat surface that is configured to generate a spatial variation in a temperature of the heat transfer surface at least when heat is provided to the heat transfer surface.
 6. The apparatus of claim 1, wherein a critical heat flux from the heat transfer surface to a liquid is greater than a critical heat flux of a heat transfer surface made from only one of said at least two materials.
 7. The apparatus of claim 1, wherein a heat transfer coefficient of the heat transfer surface is greater than a heat transfer coefficient of a heat transfer surface made from only one of said at least two materials.
 8. The apparatus of claim 1, wherein a spacing between surface portions of one of said at least two materials is from about 0.1λ_(C) to about 10λ_(C), wherein λ_(C) is a capillary length for a bubble of a predetermined liquid represented by: $\lambda_{C} = \sqrt{\frac{\sigma}{g\left( {\rho_{i} - \rho_{v}} \right)}}$ σ is a surface tension at the interface, g is the acceleration of gravity and ρ_(i) and ρ_(v) are the densities of the liquid and vapor phases of said liquid, respectively.
 9. The apparatus of claim 8, wherein a spacing between surface portions of one of said at least two materials is from about 0.5λ_(C) to about 2λ_(C).
 10. The apparatus of claim 1, wherein surface portions of each said material are rectangular or substantially rectangular in shape.
 11. The apparatus of claim 1, wherein surface portions of one said material are in the form of dots having a length of from 0.01-50 mm in a longest dimension.
 12. The apparatus of claim 11 wherein said dots have a shape selected from circular, elliptical, square, substantially circular, substantially elliptical, substantially square, rectangular, substantially rectangular or any combination of one or more of said shapes.
 13. The apparatus of claim 1, wherein the apparatus is selected from a vessel and an immersion heater.
 14. A method of boiling at least one liquid which provides increased heat transfer from a heat transfer surface of an apparatus to a liquid comprising a step of boiling said liquid in contact with an apparatus as claimed in claim
 1. 15. A method for increasing one or both of a critical heat flux from a heat transfer surface of an apparatus to a liquid and/or a heat transfer coefficient of the heat transfer surface comprising a step of providing an apparatus with the heat transfer surface as claimed in claim
 1. 16. A method of tuning a heat transfer surface of an apparatus comprising a step of forming the heat transfer surface using at least two different materials having different thermal conductivities arranged in a predetermined spatial relationship configured to further increase the critical heat flux from the heat transfer surface to a liquid and/or the heat transfer coefficient of the heat transfer surface by providing a spacing between surface portions one said material that is from about 0.1λ_(C) to about 5λ_(C), wherein λ_(C) is a capillary length of a bubble of a predetermined liquid to be boiled using said heat transfer surface.
 17. The method as claimed in claim 16, wherein the spacing between surface portions of is from 0.5λ_(C) to about 2λ_(C), wherein λ_(C) is a capillary length for a bubble of a predetermined liquid represented by: $\lambda_{C} = \sqrt{\frac{\sigma}{g\left( {\rho_{i} - \rho_{v}} \right)}}$ σ is a surface tension at the interface, g is the acceleration of gravity and ρ_(i) and ρ_(v) are the densities of the liquid and vapor phases of said liquid, respectively. 